If a ship bumps into another ship after finishing its movement it cannot target the ship it is based with in combat. Can the two ships that are based together (Say Slave I and an X-Wing) still make combat checks against other ships in their firing arcs?

Yes.

You are not allowed to shoot at a ship you are touching, but that is the only restriction when you've collided.

You cannot shoot at all if you've landed ON an asteroid, though.

I thought this was the case and just wanted to be doubly sure. Thank you for the clarification.